What is the conjecture

https://www.erdosproblems.com/865

There exists a constant $C>0$ such that, for all large $N$, if $A\subseteq \{1,\ldots,N\}$ has size at least $\frac{5}{8}N+C$ then there are distinct $a,b,c\in A$ such that $a+b,a+c,b+c\in A$.

Status: open

Choose either option

• I plan on working on this conjecture
• This issue is up for grabs: I would like to see this conjecture added by somebody else